Linear Programs are special mathematical programming problems. We understand by a mathematical programming problem in the Euclidean space ℝ n the optimization of a given real-valued function — the objective function — on a given subset of ℝ n , the so-called feasible set. A mathematical programming problem is called a linear program if its objective function is a linear functional on ℝ n and if the feasible set can be described as the intersection of finitely many halfspaces and at most finitely many hyperplanes in ℝ n . Hence the feasible set of a linear program may be represented as the solution set of a system of finitely many linear inequalities and, at most, finitely many linear equalities — the so-called (linear) constraints — in a finite number of variables.
Unable to display preview. Download preview PDF.